Abstract
LetKKbe a fixed field. We attach to each finite posetP\mathbb Pa von Neumann regularKK-algebraQK(P)Q_K(\mathbb P)in a functorial way. We show that the monoid of isomorphism classes of finitely generated projectiveQK(P)Q_K(\mathbb P)-modules is the abelian monoid generated byP\mathbb Pwith the only relations given byp=p+qp=p+qwheneverq>pq>pinP\mathbb P. This extends the class of monoids for which there is a positive solution to the realization problem for von Neumann regular rings.
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